function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta
L = ones(size(theta));
L(1, 1) = 0;

h_theta = sigmoid(X * theta);

J = (-y' * log(h_theta) - (1 - y)' * log(1 - h_theta)) / m;
J_reg = lambda / 2 / m * L' * (theta .* theta);
J = J + J_reg;

grad = (X' * ((h_theta) - y)) / m;
grad_reg = lambda / m * L .* theta;
grad = grad + grad_reg;
% =============================================================

end
